A harmless little riddle

i like it when someone discribed it as running on a treadmill and you don't feel any breeze or wind then, so why is it going to be different for an aeroplane.

LOL!!! wrote:

It is quite simple. A shame you still don't understand it.

Incidentally, the engines don't move forward. Have you forgotten the riddle already?

Here's the quote:

Pherekydes wrote:

The engines push against the air. The engines move forward.

The engines push against the air. The engines do move forward.

it's going to be different because when you're running on a treadmill, you push off of a moving surface, whereas the plane pushes on the air around it. so it would be like you on a treadmill jumping up and down with your feet and a jet pack pushing you forwards.

we know that the treadmill matches the speed of the airplane, but how do you know that this counters the force of the engines? this is a jump in logic. the treadmill exerts force on the airplane in a peculiar way--it spins the wheels. think of pulling a tablecloth out from under some dishes. the dishes don't move, because the force between the tablecloth and the dishes isn't very large.

to calculate the force of the treadmill on the airplane, you need to look at it rigorously and stop waving your hands. you can determine the force of the treadmill on the airplane by considering the torque necessary to keep the wheels spinning. once you have this torque, just divide by the radius of the wheels to get the force. then you see that this force is actually quite small compared to the force of a jet engine.

basically, people are saying that the friction between the treadmill and the airplane is as large as the force of a jet engine. this isn't right-friction has a maximum value while the jet engine does not.

and i'd like to bring up a paradox which occurs if the plane doesn't move. if the plane doesn't move, then since we know the treadmill matches the speed of the airplane, it doesn't move either. so we have a stationary airplane on a stationary treadmill with its engines on. if the plane starts to move, you're saying that the treadmill will stop it, so the treadmill with stop, too.

no, it would be like on a treadmill with your feet in contact with the ground getting pushed along by your jetpack. substitute wheels for feet and there you go.

wow. wrote:

no, it would be like on a treadmill with your feet in contact with the ground getting pushed along by your jetpack. substitute wheels for feet and there you go.

No, it would be like on a treadmill wearing rollerblades in contact with the ground, getting pushed along by your jetpack. And you'd go shooting off the front of the treadmill no matter how fast the treadmill was going. Just like the plane would. And the plane would take off after it went shooting off the front of the treadmill. Or assuming the treadmill was long enough, it would accelerate down the treadmill and take off, just like a runway. Except with the wheels spinning twice as fast.

I just got here and noticed that there are currently over 500 posts on this thread so I had to look at the original riddle. I can't believe that it has caused so much discussion. If he hadn't called it a riddle and implied that there was something tricky about it, I would hope that everyone here would understand that the plane, since it does not create forward thrust through friction with the ground but rather by propelling air behind itself, will force itself forward and take off almost as easily as it would on a regular stationary runway.

wow. wrote:

When the plane is sitting on the stationary treadmill, gravity is holding the plane to the surface of the treadmill. Now, if we start the treadmill going, the wheels are not going to just start spinning while the plane remains stationary, the plane is going to move backward with the surface of the treadmill.

The above statement is incorrect.

If you idealize the wheels as frictionless and free spinning (which is very close to the truth), unless the brakes are engaged the wheels will spin freely and the plane will remain stationary, not move backwards, once the treadmill started. Think about the axle where the wheel connects to the landing struct, not the tire contact patch on the runway. This misunderstanding is why you are misunderstanding the answer to the entire problem.

In the real world, since the wheels are not 100% frictionless, the plane will move backwards (because there is some friction force), but at nowhere near the same rate as the treadmill. If you ran the treadmill backwards (from the nose toward the tail of the plane) at 500mph, with the planes engines off, you might see the plane move backward at maybe up to 90 mph or so depending on how long you were willing to wait for the plane to accelerate (eventual drag force would stop the plane from accelerating at some speed much much less than 500mph). The wheels however would be spinning at 410mph or so.

This however becomes moot once the engines are engaged because the thrust force provided by the engines would be orders of magnitude greater than the small amount of force the treadmill could exert on the plane via friction at the wheels axel. Since the magnitude of the force propeling the plane (the engines thrust) is larger than the force acting against it (the treadmill), the plane moves foward and eventually takes off.

Thats my attempt to explain the solution. Some people it seems will never get it.

You're right that the force between the table and the dishes isn't very great. A fully-loaded 747 weighs somewhere in the area of 800,000 pounds, or about 360,000kg. Given that F=ma, 360,000kg x 9.8m/s/s = 3,528,000 Newtons. This is the force of gravity on the plane, as well as the resisting force of the treadmill at rest. I would say that is a significant force to overcome. Also, it is obvious that the engines can overcome friction, otherwise the plane couldn't move, let alone fly. That is not the issue here.

By the way, your 'paradox' doesn't even make sense. The treadmill surface is moving relative to the ground. The treadmill itself is not. The airplane on the treadmill surface is not moving either relative to the treadmill or the ground, or most importantly, the air. If the treadmill were to suddenly stop, then yes, the airplane would accelerate off the front of the treadmill.

wow. wrote:

no, it would be like on a treadmill with your feet in contact with the ground getting pushed along by your jetpack. substitute wheels for feet and there you go.

Assuming you could move keep yourself upright you would go flying off the front of the treadmill. However since you probaly couldn't turn over your legs fast enough to keep your balance you would probaly fall on your face and get pretty badly injured. Put on some rollerblades or rollerskates, and you will be much less likely to end up on your face, but you still leave the treadmill easily.

If you turn the treadmill on without turning the engine on, is the plance going to stay stationary or go backwards? If it goes backwards, are the wheels spinning or are the wheels actually not rotating but staying stationary even though the plane itself is moving backwards? Does it matter if you assume no friction of wheels to treadmill or yes friction? If there's no friction does that mean if the engines are off, the plane won't go anywhere no matter how fast the treadmill is going?

I'm just curious, I don't know enough to have an answer.

If you turn the treadmill on without turning the engine on, is the plance going to stay stationary or go backwards? If it goes backwards, are the wheels spinning or are the wheels actually not rotating but staying stationary even though the plane itself is moving backwards? Does it matter if you assume no friction of wheels to treadmill or yes friction? If there's no friction does that mean if the engines are off, the plane won't go anywhere no matter how fast the treadmill is going?

I'm just curious, I don't know enough to have an answer.

--------------------------------------------------------

If it goes backwards the wheels are actually not rotating because there is friction...

So yes it does matter if we have friction. The plane must power it's engines to over-compensate the frictional force so that it can obtain flight...

force of plane > friction + the force of treadmill

to get lift-off

Regarding the friction thing: the maximum force that the treadmill can exert on the plane is mu*m*g. So sure, give it an upper bound of 400,000N. When a plane accelerates, it reaches 100m/s in about 10 seconds, giving an acceleration of 10m/s^2, and a force of ma=400,000kg*10m/s=4,000,000N. But this is under normal circumstances, and we have no restrictions imposed on the power of our engines, so why does the acceleration have to be restricted to 10m/s^2? We could very well have an antimatter engine blasting out 4TN.

I'm a bit annoyed that you took the paradox I presented apart based on semantics. When I said the treadmill is moving, I clearly meant the treadmill surface, not the plastic frame around it. So let me be more explicit:

all of the people who say that the plane doesn't lift off agree that the plane doesn't move forwards. if the plane doesn't move forwards, then since we know the treadmill surface matches the speed of the airplane, it doesn't move either. so we have a stationary airplane on a stationary treadmill with its engines on. if the plane starts to move, you're saying that the treadmill will stop it, so the treadmill surface will stop, too.

someone who says that the plane won't lift off, explain how the treadmill can counter any amount of force the engines can produce. remember, in this riddle, the engines are arbitrarily powerful.

I interpret the question to mean that the treadmill counters the force of the engines, and so the plane cannot move forward. At all.

The wording of the question was very careful: the treadmill matches its speed to that of the airplane. Nowhere is it stated that this will counter the force of the engines.

Here is a proof of how much acceleration the treadmill would have to put out to stop the airplane. Note that this assumes that the treadmill is capable of exerting an infinitely large force.

so in a wind tunnel is the plane stationary relative to the ground but actually moving relative to the air because fans propel the air towards the plane so air is moving over the wings and the plane is actually "flying" even though relative to the ground it is not moving anywhere because some sort of anchor keeps it in place?

argh... wrote:

someone who says that the plane won't lift off, explain how the treadmill can counter any amount of force the engines can produce. remember, in this riddle, the engines are arbitrarily powerful.

This is exactly opposite what the original riddle states:

-----

An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?

-----

Airplanes exist in our daily life. Airplane engines have a maximum output and are not arbitrarily powerful. Runway-sized treadmills that are capable of running in the opposite direction at any speed an object is moving are an imaginary construct; they can be infinitely powerful.

Listen up everyone:

Think about this critically. How is the treadmill exerting force on the airplane? There are two ways:

1) Rolling resistance between the airplane wheels and the treadmill surface.

2) Friction in the axle/bearing system of the wheels.

Those are the only two forces that the treadmill imparts on the airplane. Most of you are confusing SPEED with FORCE.

I don't think it's too hard to comprehend that THOUSANDS OF POUNDS OF THRUST can overcome ROLLING RESISTANCE AND FRICTION.

Of course the plane will fly. The speed of the treadmill only serves to make the wheels spin faster, and the force from the treadmill manifests itself as rolling resistance and friction, that's it.

There is no more arguement. This is the right answer. There are no two ways about it - no "different opinions" no "different ways of looking at the question." According to the parameters of the question, the plane will take off. End of story. Period. Finito.

Relative to the air in the room, the plane is not moving at all. The laws of aerodynamics are the question here, not velocity relative to a moving plane which itself stays static. Wow, I thought I had a hard time with physics...this is just common sense.